Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should b $e ______$ t $o ______$ times of its initial length if the water is to be boiled in 15 minutes.
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Question

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should b $e ______$ t $o ______$ times of its initial length if the water is to be boiled in 15 minutes.

Options

G1 Physics · Accepted Answer

For the same supply voltage: P = V²/R For the same wire material and cross-sectional area: R ∝ ℓ Therefore: P ∝ 1/ℓ For the same amount of heat: Pt = constant So: P₁t₁ = P₂t₂ Hence: P₂/P₁ = t₁/t₂ = 20/15 = 4/3 Since P ∝ 1/ℓ: ℓ₂/ℓ₁ = P₁/P₂ = 3 4 \frac{3}{4} 4 3 ​ Therefore, the length should be decreased to 3 4 \frac{3}{4} 4 3 ​ of its initial value.

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should b e ______ t o ______ times of its initial length if the water is to be boiled in 15 minutes.

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should b e t o times of its initial length if the water is to be boiled in 15 minutes.